LMFDB - Embedded newform 804.2.q.b.625.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			625.2
Character	$\chi$	$=$	804.625
Dual form			804.2.q.b.265.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(-0.536269 + 1.17426i) q^{5} +(-0.878330 + 0.257901i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(-0.536269 + 1.17426i) q^{5} +(-0.878330 + 0.257901i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-1.94425 + 4.25731i) q^{11} +(-2.64310 - 3.05030i) q^{13} +(-1.23863 - 0.363695i) q^{15} +(-5.31227 - 3.41399i) q^{17} +(1.25176 + 0.367549i) q^{19} +(-0.380275 - 0.832687i) q^{21} +(-0.397285 - 2.76318i) q^{23} +(2.18299 + 2.51930i) q^{25} +(-0.415415 - 0.909632i) q^{27} -4.58573 q^{29} +(1.11279 - 1.28423i) q^{31} +(-4.49067 - 1.31858i) q^{33} +(0.168177 - 1.16970i) q^{35} -3.19048 q^{37} +(2.64310 - 3.05030i) q^{39} +(9.53729 + 6.12925i) q^{41} +(-9.19035 - 5.90628i) q^{43} +(0.183718 - 1.27778i) q^{45} +(1.17622 + 8.18076i) q^{47} +(-5.18382 + 3.33144i) q^{49} +(2.62322 - 5.74406i) q^{51} +(-10.8592 + 6.97877i) q^{53} +(-3.95657 - 4.56612i) q^{55} +(-0.185664 + 1.29132i) q^{57} +(0.690489 - 0.796867i) q^{59} +(-5.72413 - 12.5341i) q^{61} +(0.770092 - 0.494908i) q^{63} +(4.99927 - 1.46792i) q^{65} +(5.64310 - 5.92920i) q^{67} +(2.67852 - 0.786483i) q^{69} +(0.713125 - 0.458298i) q^{71} +(2.89894 + 6.34779i) q^{73} +(-2.18299 + 2.51930i) q^{75} +(0.609727 - 4.24074i) q^{77} +(4.15154 + 4.79113i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-2.02120 + 4.42580i) q^{83} +(6.85773 - 4.40719i) q^{85} +(-0.652618 - 4.53906i) q^{87} +(-0.858749 + 5.97273i) q^{89} +(3.10819 + 1.99751i) q^{91} +(1.42953 + 0.918703i) q^{93} +(-1.10288 + 1.27279i) q^{95} -15.7274 q^{97} +(0.666070 - 4.63262i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	−0.536269	+	1.17426i	−0.239827	+	0.525147i	−0.990824	−	0.135158i	$-0.956846\pi$
$5$	−0.536269	+	1.17426i	−0.239827	+	0.525147i	0.750997	+	0.660305i	$0.229573\pi$
$6$		0			0
$7$	−0.878330	+	0.257901i	−0.331977	+	0.0974774i	−0.443473	−	0.896287i	$-0.646254\pi$
$7$	−0.878330	+	0.257901i	−0.331977	+	0.0974774i	0.111496	+	0.993765i	$0.464436\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	−1.94425	+	4.25731i	−0.586213	+	1.28363i	0.351491	+	0.936191i	$0.385675\pi$
$11$	−1.94425	+	4.25731i	−0.586213	+	1.28363i	−0.937704	+	0.347436i	$0.887053\pi$
$12$		0			0
$13$	−2.64310	−	3.05030i	−0.733064	−	0.846001i	0.259749	−	0.965676i	$-0.416360\pi$
$13$	−2.64310	−	3.05030i	−0.733064	−	0.846001i	−0.992813	+	0.119675i	$0.961815\pi$
$14$		0			0
$15$	−1.23863	−	0.363695i	−0.319813	−	0.0939057i
$16$		0			0
$17$	−5.31227	−	3.41399i	−1.28841	−	0.828013i	−0.296513	−	0.955029i	$-0.595824\pi$
$17$	−5.31227	−	3.41399i	−1.28841	−	0.828013i	−0.991901	+	0.127016i	$0.959460\pi$
$18$		0			0
$19$	1.25176	+	0.367549i	0.287173	+	0.0843215i	0.422146	−	0.906528i	$-0.361277\pi$
$19$	1.25176	+	0.367549i	0.287173	+	0.0843215i	−0.134974	+	0.990849i	$0.543095\pi$
$20$		0			0
$21$	−0.380275	−	0.832687i	−0.0829829	−	0.181707i
$22$		0			0
$23$	−0.397285	−	2.76318i	−0.0828397	−	0.576163i	−0.988392	−	0.151928i	$-0.951452\pi$
$23$	−0.397285	−	2.76318i	−0.0828397	−	0.576163i	0.905552	−	0.424236i	$-0.139457\pi$
$24$		0			0
$25$	2.18299	+	2.51930i	0.436598	+	0.503861i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	−4.58573			−0.851549			−0.425774	−	0.904829i	$-0.639998\pi$
$29$	−4.58573			−0.851549			−0.425774	+	0.904829i	$0.639998\pi$
$30$		0			0
$31$	1.11279	−	1.28423i	0.199864	−	0.230655i	−0.646966	−	0.762519i	$-0.723963\pi$
$31$	1.11279	−	1.28423i	0.199864	−	0.230655i	0.846830	+	0.531863i	$0.178508\pi$
$32$		0			0
$33$	−4.49067	−	1.31858i	−0.781725	−	0.229535i
$34$		0			0
$35$	0.168177	−	1.16970i	0.0284271	−	0.197715i
$36$		0			0
$37$	−3.19048			−0.524512			−0.262256	−	0.964998i	$-0.584467\pi$
$37$	−3.19048			−0.524512			−0.262256	+	0.964998i	$0.584467\pi$
$38$		0			0
$39$	2.64310	−	3.05030i	0.423235	−	0.488439i
$40$		0			0
$41$	9.53729	+	6.12925i	1.48947	+	0.957227i	0.996176	+	0.0873675i	$0.0278454\pi$
$41$	9.53729	+	6.12925i	1.48947	+	0.957227i	0.493299	+	0.869860i	$0.335791\pi$
$42$		0			0
$43$	−9.19035	−	5.90628i	−1.40152	−	0.900699i	−0.401630	−	0.915802i	$-0.631556\pi$
$43$	−9.19035	−	5.90628i	−1.40152	−	0.900699i	−0.999886	+	0.0151027i	$0.995192\pi$
$44$		0			0
$45$	0.183718	−	1.27778i	0.0273870	−	0.190481i
$46$		0			0
$47$	1.17622	+	8.18076i	0.171569	+	1.19329i	0.875571	+	0.483089i	$0.160485\pi$
$47$	1.17622	+	8.18076i	0.171569	+	1.19329i	−0.704003	+	0.710197i	$0.748606\pi$
$48$		0			0
$49$	−5.18382	+	3.33144i	−0.740546	+	0.475920i
$50$		0			0
$51$	2.62322	−	5.74406i	0.367325	−	0.804329i
$52$		0			0
$53$	−10.8592	+	6.97877i	−1.49162	+	0.958607i	−0.495690	+	0.868499i	$0.665085\pi$
$53$	−10.8592	+	6.97877i	−1.49162	+	0.958607i	−0.995932	+	0.0901079i	$0.971279\pi$
$54$		0			0
$55$	−3.95657	−	4.56612i	−0.533504	−	0.615696i
$56$		0			0
$57$	−0.185664	+	1.29132i	−0.0245918	+	0.171040i
$58$		0			0
$59$	0.690489	−	0.796867i	0.0898940	−	0.103743i	−0.709020	−	0.705188i	$-0.750863\pi$
$59$	0.690489	−	0.796867i	0.0898940	−	0.103743i	0.798914	+	0.601445i	$0.205408\pi$
$60$		0			0
$61$	−5.72413	−	12.5341i	−0.732900	−	1.60483i	−0.794893	−	0.606750i	$-0.792473\pi$
$61$	−5.72413	−	12.5341i	−0.732900	−	1.60483i	0.0619934	−	0.998077i	$-0.480254\pi$
$62$		0			0
$63$	0.770092	−	0.494908i	0.0970225	−	0.0623526i
$64$		0			0
$65$	4.99927	−	1.46792i	0.620084	−	0.182073i
$66$		0			0
$67$	5.64310	−	5.92920i	0.689415	−	0.724367i
$67$	5.64310	−	5.92920i	0.689415	−	0.724367i
$68$		0			0
$69$	2.67852	−	0.786483i	0.322455	−	0.0946815i
$70$		0			0
$71$	0.713125	−	0.458298i	0.0846324	−	0.0543899i	−0.497640	−	0.867384i	$-0.665800\pi$
$71$	0.713125	−	0.458298i	0.0846324	−	0.0543899i	0.582273	+	0.812994i	$0.302164\pi$
$72$		0			0
$73$	2.89894	+	6.34779i	0.339295	+	0.742953i	0.999970	−	0.00771910i	$-0.00245709\pi$
$73$	2.89894	+	6.34779i	0.339295	+	0.742953i	−0.660675	+	0.750672i	$0.729730\pi$
$74$		0			0
$75$	−2.18299	+	2.51930i	−0.252070	+	0.290904i
$76$		0			0
$77$	0.609727	−	4.24074i	0.0694848	−	0.483278i
$78$		0			0
$79$	4.15154	+	4.79113i	0.467084	+	0.539044i	0.939598	−	0.342279i	$-0.111199\pi$
$79$	4.15154	+	4.79113i	0.467084	+	0.539044i	−0.472514	+	0.881323i	$0.656653\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−2.02120	+	4.42580i	−0.221855	+	0.485795i	−0.987530	−	0.157433i	$-0.949678\pi$
$83$	−2.02120	+	4.42580i	−0.221855	+	0.485795i	0.765674	+	0.643228i	$0.222405\pi$
$84$		0			0
$85$	6.85773	−	4.40719i	0.743825	−	0.478027i
$86$		0			0
$87$	−0.652618	−	4.53906i	−0.0699680	−	0.486638i
$88$		0			0
$89$	−0.858749	+	5.97273i	−0.0910272	+	0.633108i	0.892324	+	0.451395i	$0.149073\pi$
$89$	−0.858749	+	5.97273i	−0.0910272	+	0.633108i	−0.983352	+	0.181713i	$0.941836\pi$
$90$		0			0
$91$	3.10819	+	1.99751i	0.325827	+	0.209396i
$92$		0			0
$93$	1.42953	+	0.918703i	0.148235	+	0.0952650i
$94$		0			0
$95$	−1.10288	+	1.27279i	−0.113153	+	0.130585i
$96$		0			0
$97$	−15.7274			−1.59688			−0.798438	−	0.602078i	$-0.794340\pi$
$97$	−15.7274			−1.59688			−0.798438	+	0.602078i	$0.794340\pi$
$98$		0			0
$99$	0.666070	−	4.63262i	0.0669425	−	0.465595i
$100$		0			0
$101$	−11.0344	−	3.24000i	−1.09797	−	0.322392i	−0.317922	−	0.948117i	$-0.602985\pi$
$101$	−11.0344	−	3.24000i	−1.09797	−	0.322392i	−0.780044	+	0.625725i	$0.784803\pi$
$102$		0			0
$103$	2.19063	−	2.52813i	0.215850	−	0.249104i	−0.637491	−	0.770458i	$-0.720028\pi$
$103$	2.19063	−	2.52813i	0.215850	−	0.249104i	0.853340	+	0.521354i	$0.174573\pi$
$104$		0			0
$105$	1.18172			0.115325
$106$		0			0
$107$	7.37899	+	16.1577i	0.713354	+	1.56203i	0.822990	+	0.568056i	$0.192304\pi$
$107$	7.37899	+	16.1577i	0.713354	+	1.56203i	−0.109636	+	0.993972i	$0.534968\pi$
$108$		0			0
$109$	12.2705	+	14.1609i	1.17530	+	1.35637i	0.921151	+	0.389205i	$0.127250\pi$
$109$	12.2705	+	14.1609i	1.17530	+	1.35637i	0.254150	+	0.967165i	$0.418204\pi$
$110$		0			0
$111$	−0.454053	−	3.15801i	−0.0430968	−	0.299745i
$112$		0			0
$113$	−0.221563	−	0.485156i	−0.0208429	−	0.0456397i	0.898924	−	0.438104i	$-0.144350\pi$
$113$	−0.221563	−	0.485156i	−0.0208429	−	0.0456397i	−0.919767	+	0.392464i	$0.871623\pi$
$114$		0			0
$115$	3.45776	+	1.01529i	0.322438	+	0.0946762i
$116$		0			0
$117$	3.39541	+	2.18209i	0.313905	+	0.201735i
$118$		0			0
$119$	5.54639	+	1.62857i	0.508437	+	0.149291i
$120$		0			0
$121$	−7.14111	−	8.24128i	−0.649192	−	0.749207i
$122$		0			0
$123$	−4.70956	+	10.3125i	−0.424647	+	0.929847i
$124$		0			0
$125$	−10.3222	+	3.03086i	−0.923242	+	0.271088i
$126$		0			0
$127$	14.5727	−	4.27893i	1.29312	−	0.379693i	0.438396	−	0.898782i	$-0.355547\pi$
$127$	14.5727	−	4.27893i	1.29312	−	0.379693i	0.854721	+	0.519088i	$0.173728\pi$
$128$		0			0
$129$	4.53824	−	9.93736i	0.399570	−	0.874936i
$130$		0			0
$131$	2.05195	+	14.2716i	0.179279	+	1.24691i	0.858436	+	0.512921i	$0.171437\pi$
$131$	2.05195	+	14.2716i	0.179279	+	1.24691i	−0.679156	+	0.733994i	$0.737654\pi$
$132$		0			0
$133$	−1.19425			−0.103554
$134$		0			0
$135$	1.29092			0.111105
$136$		0			0
$137$	0.363829	+	2.53049i	0.0310840	+	0.216194i	0.999443	−	0.0333665i	$-0.0106229\pi$
$137$	0.363829	+	2.53049i	0.0310840	+	0.216194i	−0.968359	+	0.249561i	$0.919714\pi$
$138$		0			0
$139$	2.84479	−	6.22922i	0.241292	−	0.528356i	−0.749779	−	0.661688i	$-0.769840\pi$
$139$	2.84479	−	6.22922i	0.241292	−	0.528356i	0.991071	+	0.133332i	$0.0425677\pi$
$140$		0			0
$141$	−7.93009	+	2.32849i	−0.667834	+	0.196094i
$142$		0			0
$143$	18.1249	−	5.32195i	1.51568	−	0.445044i
$144$		0			0
$145$	2.45918	−	5.38486i	0.204224	−	0.447189i
$146$		0			0
$147$	−4.03527	−	4.65695i	−0.332823	−	0.384098i
$148$		0			0
$149$	2.77897	+	0.815978i	0.227662	+	0.0668475i	0.393574	−	0.919293i	$-0.371239\pi$
$149$	2.77897	+	0.815978i	0.227662	+	0.0668475i	−0.165912	+	0.986141i	$0.553057\pi$
$150$		0			0
$151$	12.3713	+	7.95055i	1.00676	+	0.647006i	0.936553	−	0.350526i	$-0.113997\pi$
$151$	12.3713	+	7.95055i	1.00676	+	0.647006i	0.0702086	+	0.997532i	$0.477633\pi$
$152$		0			0
$153$	6.05891	+	1.77906i	0.489834	+	0.143828i
$154$		0			0
$155$	0.911273	+	1.99541i	0.0731952	+	0.160275i
$156$		0			0
$157$	0.319653	+	2.22324i	0.0255111	+	0.177434i	0.998593	−	0.0530253i	$-0.0168864\pi$
$157$	0.319653	+	2.22324i	0.0255111	+	0.177434i	−0.973082	+	0.230459i	$0.925977\pi$
$158$		0			0
$159$	−8.45315	−	9.75546i	−0.670379	−	0.773658i
$160$		0			0
$161$	1.06157	+	2.32452i	0.0836638	+	0.183198i
$162$		0			0
$163$	−18.7620			−1.46955			−0.734775	−	0.678311i	$-0.762712\pi$
$163$	−18.7620			−1.46955			−0.734775	+	0.678311i	$0.762712\pi$
$164$		0			0
$165$	3.95657	−	4.56612i	0.308018	−	0.355472i
$166$		0			0
$167$	11.4524	+	3.36274i	0.886215	+	0.260216i	0.692998	−	0.720940i	$-0.256290\pi$
$167$	11.4524	+	3.36274i	0.886215	+	0.260216i	0.193218	+	0.981156i	$0.438108\pi$
$168$		0			0
$169$	−0.468261	+	3.25682i	−0.0360200	+	0.250525i
$170$		0			0
$171$	−1.30460			−0.0997655
$172$		0			0
$173$	12.1753	−	14.0510i	0.925669	−	1.06828i	−0.0718167	−	0.997418i	$-0.522880\pi$
$173$	12.1753	−	14.0510i	0.925669	−	1.06828i	0.997486	−	0.0708617i	$-0.0225749\pi$
$174$		0			0
$175$	−2.56712	−	1.64979i	−0.194056	−	0.124712i
$176$		0			0
$177$	0.887022	+	0.570055i	0.0666727	+	0.0428479i
$178$		0			0
$179$	−0.247637	+	1.72235i	−0.0185093	+	0.128735i	−0.996981	−	0.0776462i	$-0.975260\pi$
$179$	−0.247637	+	1.72235i	−0.0185093	+	0.128735i	0.978472	+	0.206381i	$0.0661686\pi$
$180$		0			0
$181$	1.26330	+	8.78646i	0.0939005	+	0.653092i	0.981356	+	0.192199i	$0.0615619\pi$
$181$	1.26330	+	8.78646i	0.0939005	+	0.653092i	−0.887455	+	0.460893i	$0.847529\pi$
$182$		0			0
$183$	11.5919	−	7.44965i	0.856897	−	0.550694i
$184$		0			0
$185$	1.71096	−	3.74647i	0.125792	−	0.275446i
$186$		0			0
$187$	24.8628	−	15.9783i	1.81814	−	1.16845i
$188$		0			0
$189$	0.599466	+	0.691821i	0.0436048	+	0.0503226i
$190$		0			0
$191$	−0.695824	+	4.83956i	−0.0503481	+	0.350179i	0.949039	+	0.315160i	$0.102058\pi$
$191$	−0.695824	+	4.83956i	−0.0503481	+	0.350179i	−0.999387	+	0.0350187i	$0.988851\pi$
$192$		0			0
$193$	−9.99031	+	11.5294i	−0.719118	+	0.829906i	−0.991201	−	0.132367i	$-0.957742\pi$
$193$	−9.99031	+	11.5294i	−0.719118	+	0.829906i	0.272083	+	0.962274i	$0.412288\pi$
$194$		0			0
$195$	2.16445	+	4.73948i	0.154999	+	0.339401i
$196$		0			0
$197$	−9.60601	+	6.17341i	−0.684400	+	0.439837i	−0.836091	−	0.548591i	$-0.815164\pi$
$197$	−9.60601	+	6.17341i	−0.684400	+	0.439837i	0.151691	+	0.988428i	$0.451528\pi$
$198$		0			0
$199$	1.68870	−	0.495846i	0.119709	−	0.0351496i	−0.221330	−	0.975199i	$-0.571040\pi$
$199$	1.68870	−	0.495846i	0.119709	−	0.0351496i	0.341038	+	0.940049i	$0.389221\pi$
$200$		0			0
$201$	6.67194	+	4.74185i	0.470603	+	0.334464i
$202$		0			0
$203$	4.02779	−	1.18266i	0.282695	−	0.0830068i
$204$		0			0
$205$	−12.3119	+	7.91239i	−0.859901	+	0.552625i
$206$		0			0
$207$	1.15967	+	2.53932i	0.0806027	+	0.176495i
$208$		0			0
$209$	−3.99850	+	4.61451i	−0.276582	+	0.319192i
$210$		0			0
$211$	1.35955	−	9.45589i	0.0935954	−	0.650970i	−0.887978	−	0.459886i	$-0.847890\pi$
$211$	1.35955	−	9.45589i	0.0935954	−	0.650970i	0.981574	−	0.191085i	$-0.0612005\pi$
$212$		0			0
$213$	0.555121	+	0.640644i	0.0380363	+	0.0438962i
$214$		0			0
$215$	11.8640	−	7.62455i	0.809121	−	0.519990i
$216$		0			0
$217$	−0.646196	+	1.41497i	−0.0438666	+	0.0960545i
$218$		0			0
$219$	−5.87062	+	3.77282i	−0.396700	+	0.254943i
$220$		0			0
$221$	3.62717	+	25.2275i	0.243990	+	1.69699i
$222$		0			0
$223$	2.92842	−	20.3676i	0.196101	−	1.36391i	−0.619362	−	0.785106i	$-0.712609\pi$
$223$	2.92842	−	20.3676i	0.196101	−	1.36391i	0.815463	−	0.578809i	$-0.196482\pi$
$224$		0			0
$225$	−2.80433	−	1.80224i	−0.186956	−	0.120149i
$226$		0			0
$227$	21.7603	+	13.9845i	1.44428	+	0.928184i	0.999470	+	0.0325608i	$0.0103663\pi$
$227$	21.7603	+	13.9845i	1.44428	+	0.928184i	0.444813	+	0.895623i	$0.353270\pi$
$228$		0			0
$229$	8.12663	−	9.37863i	0.537023	−	0.619757i	−0.420787	−	0.907159i	$-0.638246\pi$
$229$	8.12663	−	9.37863i	0.537023	−	0.619757i	0.957810	+	0.287402i	$0.0927916\pi$
$230$		0			0
$231$	4.28435			0.281890
$232$		0			0
$233$	−0.783459	+	5.44908i	−0.0513261	+	0.356981i	0.947932	+	0.318472i	$0.103170\pi$
$233$	−0.783459	+	5.44908i	−0.0513261	+	0.356981i	−0.999258	+	0.0385086i	$0.987739\pi$
$234$		0			0
$235$	−10.2371	−	3.00590i	−0.667797	−	0.196083i
$236$		0			0
$237$	−4.15154	+	4.79113i	−0.269671	+	0.311217i
$238$		0			0
$239$	−17.6365			−1.14081			−0.570406	−	0.821363i	$-0.693214\pi$
$239$	−17.6365			−1.14081			−0.570406	+	0.821363i	$0.693214\pi$
$240$		0			0
$241$	10.5756	+	23.1572i	0.681231	+	1.49169i	0.861333	+	0.508041i	$0.169630\pi$
$241$	10.5756	+	23.1572i	0.681231	+	1.49169i	−0.180102	+	0.983648i	$0.557643\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	−1.13207	−	7.87373i	−0.0723254	−	0.503034i
$246$		0			0
$247$	−2.18738	−	4.78970i	−0.139180	−	0.304762i
$248$		0			0
$249$	−4.66840	−	1.37077i	−0.295848	−	0.0868688i
$250$		0			0
$251$	−0.539104	−	0.346461i	−0.0340280	−	0.0218684i	0.523516	−	0.852016i	$-0.324620\pi$
$251$	−0.539104	−	0.346461i	−0.0340280	−	0.0218684i	−0.557544	+	0.830147i	$0.688256\pi$
$252$		0			0
$253$	12.5361	+	3.68094i	0.788140	+	0.231419i
$254$		0			0
$255$	5.33829	+	6.16072i	0.334297	+	0.385799i
$256$		0			0
$257$	8.04521	−	17.6166i	0.501847	−	1.09889i	−0.474018	−	0.880515i	$-0.657197\pi$
$257$	8.04521	−	17.6166i	0.501847	−	1.09889i	0.975865	−	0.218376i	$-0.0700758\pi$
$258$		0			0
$259$	2.80230	−	0.822829i	0.174126	−	0.0511281i
$260$		0			0
$261$	4.39998	−	1.29195i	0.272352	−	0.0799697i
$262$		0			0
$263$	10.6614	−	23.3452i	0.657409	−	1.43952i	−0.227508	−	0.973776i	$-0.573058\pi$
$263$	10.6614	−	23.3452i	0.657409	−	1.43952i	0.884917	−	0.465748i	$-0.154215\pi$
$264$		0			0
$265$	−2.37149	−	16.4940i	−0.145679	−	1.01322i
$266$		0			0
$267$	−6.03415			−0.369284
$268$		0			0
$269$	−17.6429			−1.07571			−0.537854	−	0.843038i	$-0.680765\pi$
$269$	−17.6429			−1.07571			−0.537854	+	0.843038i	$0.680765\pi$
$270$		0			0
$271$	1.54182	+	10.7236i	0.0936586	+	0.651410i	0.981529	+	0.191316i	$0.0612754\pi$
$271$	1.54182	+	10.7236i	0.0936586	+	0.651410i	−0.887870	+	0.460094i	$0.847816\pi$
$272$		0			0
$273$	−1.53484	+	3.36083i	−0.0928927	+	0.203407i
$274$		0			0
$275$	−14.9697	+	4.39551i	−0.902709	+	0.265059i
$276$		0			0
$277$	17.8315	−	5.23580i	1.07139	−	0.314589i	0.301961	−	0.953320i	$-0.402359\pi$
$277$	17.8315	−	5.23580i	1.07139	−	0.314589i	0.769429	+	0.638732i	$0.220541\pi$
$278$		0			0
$279$	−0.705908	+	1.54572i	−0.0422616	+	0.0925401i
$280$		0			0
$281$	−4.54316	−	5.24308i	−0.271022	−	0.312776i	0.603881	−	0.797075i	$-0.293620\pi$
$281$	−4.54316	−	5.24308i	−0.271022	−	0.312776i	−0.874903	+	0.484299i	$0.839075\pi$
$282$		0			0
$283$	−10.8588	−	3.18842i	−0.645486	−	0.189532i	−0.0574269	−	0.998350i	$-0.518290\pi$
$283$	−10.8588	−	3.18842i	−0.645486	−	0.189532i	−0.588059	+	0.808818i	$0.700108\pi$
$284$		0			0
$285$	−1.41679	−	0.910516i	−0.0839234	−	0.0539343i
$286$		0			0
$287$	−9.95763	−	2.92382i	−0.587780	−	0.172588i
$288$		0			0
$289$	9.50281	+	20.8083i	0.558989	+	1.22402i
$290$		0			0
$291$	−2.23824	−	15.5673i	−0.131208	−	0.912572i
$292$		0			0
$293$	−22.3591	−	25.8038i	−1.30623	−	1.50747i	−0.708248	−	0.705964i	$-0.750514\pi$
$293$	−22.3591	−	25.8038i	−1.30623	−	1.50747i	−0.597984	−	0.801508i	$-0.704031\pi$
$294$		0			0
$295$	0.565445	+	1.23815i	0.0329215	+	0.0720880i
$296$		0			0
$297$	4.68025			0.271576
$298$		0			0
$299$	−7.37847	+	8.51520i	−0.426708	+	0.492447i
$300$		0			0
$301$	9.59540	+	2.81746i	0.553069	+	0.162396i
$302$		0			0
$303$	1.63666	−	11.3832i	0.0940236	−	0.653948i
$304$		0			0
$305$	17.7880			1.01854
$306$		0			0
$307$	−14.3693	+	16.5830i	−0.820099	+	0.946445i	−0.999302	−	0.0373676i	$-0.988103\pi$
$307$	−14.3693	+	16.5830i	−0.820099	+	0.946445i	0.179203	+	0.983812i	$0.442648\pi$
$308$		0			0
$309$	2.81415	+	1.80855i	0.160092	+	0.102885i
$310$		0			0
$311$	−4.77241	−	3.06704i	−0.270618	−	0.173916i	0.398293	−	0.917258i	$-0.369603\pi$
$311$	−4.77241	−	3.06704i	−0.270618	−	0.173916i	−0.668911	+	0.743343i	$0.733239\pi$
$312$		0			0
$313$	−0.217998	+	1.51621i	−0.0123220	+	0.0857013i	−0.995054	−	0.0993308i	$-0.968330\pi$
$313$	−0.217998	+	1.51621i	−0.0123220	+	0.0857013i	0.982732	+	0.185032i	$0.0592389\pi$
$314$		0			0
$315$	0.168177	+	1.16970i	0.00947570	+	0.0659049i
$316$		0			0
$317$	9.95310	−	6.39647i	0.559022	−	0.359262i	−0.230416	−	0.973092i	$-0.574009\pi$
$317$	9.95310	−	6.39647i	0.559022	−	0.359262i	0.789438	+	0.613831i	$0.210372\pi$
$318$		0			0
$319$	8.91580	−	19.5229i	0.499189	−	1.09307i
$320$		0			0
$321$	−14.9431	+	9.60337i	−0.834045	+	0.536008i
$322$		0			0
$323$	−5.39486	−	6.22600i	−0.300178	−	0.346424i
$324$		0			0
$325$	1.91477	−	13.3176i	0.106213	−	0.738725i
$326$		0			0
$327$	−12.2705	+	14.1609i	−0.678560	+	0.783100i
$328$		0			0
$329$	−3.14293	−	6.88205i	−0.173275	−	0.379420i
$330$		0			0
$331$	−15.8023	+	10.1555i	−0.868574	+	0.558199i	−0.897316	−	0.441388i	$-0.854486\pi$
$331$	−15.8023	+	10.1555i	−0.868574	+	0.558199i	0.0287421	+	0.999587i	$0.490850\pi$
$332$		0			0
$333$	3.06125	−	0.898863i	0.167755	−	0.0492574i
$334$		0			0
$335$	3.93623	+	9.80614i	0.215059	+	0.535767i
$336$		0			0
$337$	−9.09726	+	2.67120i	−0.495559	+	0.145509i	−0.519956	−	0.854193i	$-0.674052\pi$
$337$	−9.09726	+	2.67120i	−0.495559	+	0.145509i	0.0243968	+	0.999702i	$0.492233\pi$
$338$		0			0
$339$	0.448686	−	0.288353i	0.0243693	−	0.0156612i
$340$		0			0
$341$	3.30383	+	7.23438i	0.178912	+	0.391764i
$342$		0			0
$343$	7.89019	−	9.10577i	0.426030	−	0.491665i
$344$		0			0
$345$	−0.512865	+	3.56705i	−0.0276117	+	0.192044i
$346$		0			0
$347$	−3.54827	−	4.09492i	−0.190481	−	0.219827i	0.652474	−	0.757812i	$-0.273731\pi$
$347$	−3.54827	−	4.09492i	−0.190481	−	0.219827i	−0.842955	+	0.537984i	$0.819186\pi$
$348$		0			0
$349$	8.19562	−	5.26700i	0.438701	−	0.281936i	−0.302589	−	0.953121i	$-0.597851\pi$
$349$	8.19562	−	5.26700i	0.438701	−	0.281936i	0.741290	+	0.671185i	$0.234214\pi$
$350$		0			0
$351$	−1.67667	+	3.67139i	−0.0894939	+	0.195964i
$352$		0			0
$353$	−15.8570	+	10.1907i	−0.843985	+	0.542396i	−0.889693	−	0.456559i	$-0.849082\pi$
$353$	−15.8570	+	10.1907i	−0.843985	+	0.542396i	0.0457083	+	0.998955i	$0.485446\pi$
$354$		0			0
$355$	0.155736	+	1.08317i	0.00826562	+	0.0574886i
$356$		0			0
$357$	−0.822657	+	5.72171i	−0.0435396	+	0.302825i
$358$		0			0
$359$	1.41898	+	0.911924i	0.0748910	+	0.0481295i	0.577550	−	0.816355i	$-0.304009\pi$
$359$	1.41898	+	0.911924i	0.0748910	+	0.0481295i	−0.502659	+	0.864485i	$0.667645\pi$
$360$		0			0
$361$	−14.5520	−	9.35201i	−0.765895	−	0.492211i
$362$		0			0
$363$	7.14111	−	8.24128i	0.374811	−	0.432555i
$364$		0			0
$365$	−9.00860			−0.471532
$366$		0			0
$367$	−1.94807	+	13.5491i	−0.101688	+	0.707258i	0.873652	+	0.486552i	$0.161745\pi$
$367$	−1.94807	+	13.5491i	−0.101688	+	0.707258i	−0.975340	+	0.220707i	$0.929164\pi$
$368$		0			0
$369$	−10.8778	−	3.19400i	−0.566274	−	0.166273i
$370$		0			0
$371$	7.73811	−	8.93025i	0.401742	−	0.463635i
$372$		0			0
$373$	−30.3720			−1.57260			−0.786302	−	0.617842i	$-0.788007\pi$
$373$	−30.3720			−1.57260			−0.786302	+	0.617842i	$0.788007\pi$
$374$		0			0
$375$	−4.46901	−	9.78576i	−0.230778	−	0.505334i
$376$		0			0
$377$	12.1205	+	13.9879i	0.624240	+	0.720411i
$378$		0			0
$379$	0.921830	+	6.41147i	0.0473512	+	0.329335i	0.999704	+	0.0243359i	$0.00774712\pi$
$379$	0.921830	+	6.41147i	0.0473512	+	0.329335i	−0.952353	+	0.304999i	$0.901344\pi$
$380$		0			0
$381$	6.30928	+	13.8154i	0.323234	+	0.707785i
$382$		0			0
$383$	−5.28953	−	1.55315i	−0.270282	−	0.0793621i	0.143783	−	0.989609i	$-0.454073\pi$
$383$	−5.28953	−	1.55315i	−0.270282	−	0.0793621i	−0.414065	+	0.910247i	$0.635891\pi$
$384$		0			0
$385$	4.65278	+	2.99016i	0.237128	+	0.152393i
$386$		0			0
$387$	10.4821	+	3.07781i	0.532834	+	0.156454i
$388$		0			0
$389$	0.154633	+	0.178456i	0.00784021	+	0.00904808i	0.759656	−	0.650325i	$-0.225367\pi$
$389$	0.154633	+	0.178456i	0.00784021	+	0.00904808i	−0.751816	+	0.659373i	$0.770822\pi$
$390$		0			0
$391$	−7.32298	+	16.0351i	−0.370339	+	0.810929i
$392$		0			0
$393$	−13.8343	+	4.06212i	−0.697848	+	0.204907i
$394$		0			0
$395$	−7.85240	+	2.30567i	−0.395097	+	0.116011i
$396$		0			0
$397$	−1.72141	+	3.76936i	−0.0863949	+	0.189179i	−0.947898	−	0.318574i	$-0.896796\pi$
$397$	−1.72141	+	3.76936i	−0.0863949	+	0.189179i	0.861503	+	0.507752i	$0.169523\pi$
$398$		0			0
$399$	−0.169959	−	1.18209i	−0.00850859	−	0.0591786i
$400$		0			0
$401$	−36.4984			−1.82264			−0.911322	−	0.411694i	$-0.864937\pi$
$401$	−36.4984			−1.82264			−0.911322	+	0.411694i	$0.864937\pi$
$402$		0			0
$403$	−6.85853			−0.341648
$404$		0			0
$405$	0.183718	+	1.27778i	0.00912900	+	0.0634936i
$406$		0			0
$407$	6.20309	−	13.5829i	0.307476	−	0.673278i
$408$		0			0
$409$	24.7894	−	7.27882i	1.22576	−	0.359914i	0.396109	−	0.918203i	$-0.370360\pi$
$409$	24.7894	−	7.27882i	1.22576	−	0.359914i	0.829646	+	0.558289i	$0.188542\pi$
$410$		0			0
$411$	−2.45295	+	0.720252i	−0.120995	+	0.0355274i
$412$		0			0
$413$	−0.400964	+	0.877989i	−0.0197302	+	0.0432030i
$414$		0			0
$415$	−4.11316	−	4.74684i	−0.201907	−	0.233013i
$416$		0			0
$417$	6.57068	+	1.92932i	0.321767	+	0.0944794i
$418$		0			0
$419$	6.27243	+	4.03105i	0.306428	+	0.196930i	0.684813	−	0.728719i	$-0.259884\pi$
$419$	6.27243	+	4.03105i	0.306428	+	0.196930i	−0.378385	+	0.925649i	$0.623520\pi$
$420$		0			0
$421$	−33.0784	−	9.71269i	−1.61214	−	0.473368i	−0.653251	−	0.757142i	$-0.726595\pi$
$421$	−33.0784	−	9.71269i	−1.61214	−	0.473368i	−0.958891	+	0.283774i	$0.908413\pi$
$422$		0			0
$423$	−3.43336	−	7.51800i	−0.166935	−	0.365538i
$424$		0			0
$425$	−2.99575	−	20.8359i	−0.145315	−	1.01069i
$426$		0			0
$427$	8.26023	+	9.53281i	0.399740	+	0.461325i
$428$		0			0
$429$	7.84723	+	17.1830i	0.378868	+	0.829605i
$430$		0			0
$431$	2.41518			0.116335			0.0581677	−	0.998307i	$-0.481474\pi$
$431$	2.41518			0.116335			0.0581677	+	0.998307i	$0.481474\pi$
$432$		0			0
$433$	−2.58300	+	2.98095i	−0.124131	+	0.143255i	−0.814413	−	0.580285i	$-0.802941\pi$
$433$	−2.58300	+	2.98095i	−0.124131	+	0.143255i	0.690282	+	0.723540i	$0.257486\pi$
$434$		0			0
$435$	5.68003	+	1.66781i	0.272337	+	0.0799653i
$436$		0			0
$437$	0.518300	−	3.60485i	0.0247936	−	0.172443i
$438$		0			0
$439$	−39.4321			−1.88199			−0.940996	−	0.338419i	$-0.890108\pi$
$439$	−39.4321			−1.88199			−0.940996	+	0.338419i	$0.890108\pi$
$440$		0			0
$441$	4.03527	−	4.65695i	0.192156	−	0.221759i
$442$		0			0
$443$	−9.38461	−	6.03113i	−0.445876	−	0.286547i	0.298373	−	0.954449i	$-0.403556\pi$
$443$	−9.38461	−	6.03113i	−0.445876	−	0.286547i	−0.744249	+	0.667902i	$0.767193\pi$
$444$		0			0
$445$	−6.55305	−	4.21139i	−0.310644	−	0.199639i
$446$		0			0
$447$	−0.412184	+	2.86681i	−0.0194957	+	0.135595i
$448$		0			0
$449$	−2.10295	−	14.6264i	−0.0992446	−	0.690261i	−0.977324	−	0.211747i	$-0.932085\pi$
$449$	−2.10295	−	14.6264i	−0.0992446	−	0.690261i	0.878080	−	0.478514i	$-0.158824\pi$
$450$		0			0
$451$	−44.6370	+	28.6864i	−2.10187	+	1.35079i
$452$		0			0
$453$	−6.10900	+	13.3769i	−0.287026	+	0.628499i
$454$		0			0
$455$	−4.01243	+	2.57863i	−0.188106	+	0.120888i
$456$		0			0
$457$	−5.81019	−	6.70531i	−0.271789	−	0.313661i	0.603403	−	0.797436i	$-0.293811\pi$
$457$	−5.81019	−	6.70531i	−0.271789	−	0.313661i	−0.875193	+	0.483775i	$0.839265\pi$
$458$		0			0
$459$	−0.898676	+	6.25043i	−0.0419466	+	0.291745i
$460$		0			0
$461$	11.1451	−	12.8621i	0.519077	−	0.599047i	−0.434322	−	0.900758i	$-0.643012\pi$
$461$	11.1451	−	12.8621i	0.519077	−	0.599047i	0.953400	+	0.301710i	$0.0975576\pi$
$462$		0			0
$463$	−4.73052	−	10.3584i	−0.219846	−	0.481395i	0.767286	−	0.641305i	$-0.221607\pi$
$463$	−4.73052	−	10.3584i	−0.219846	−	0.481395i	−0.987132	+	0.159910i	$0.948880\pi$
$464$		0			0
$465$	−1.84541	+	1.18597i	−0.0855789	+	0.0549982i
$466$		0			0
$467$	−16.7589	+	4.92085i	−0.775509	+	0.227710i	−0.645456	−	0.763797i	$-0.723333\pi$
$467$	−16.7589	+	4.92085i	−0.775509	+	0.227710i	−0.130052	+	0.991507i	$0.541515\pi$
$468$		0			0
$469$	−3.42736	+	6.66315i	−0.158261	+	0.307676i
$470$		0			0
$471$	−2.15512	+	0.632799i	−0.0993025	+	0.0291578i
$472$		0			0
$473$	43.0132	−	27.6429i	1.97775	−	1.27102i
$474$		0			0
$475$	1.80660	+	3.95591i	0.0828927	+	0.181510i
$476$		0			0
$477$	8.45315	−	9.75546i	0.387043	−	0.446672i
$478$		0			0
$479$	1.37595	−	9.56996i	0.0628689	−	0.437262i	−0.933940	−	0.357431i	$-0.883653\pi$
$479$	1.37595	−	9.56996i	0.0628689	−	0.437262i	0.996808	−	0.0798314i	$-0.0254382\pi$
$480$		0			0
$481$	8.43277	+	9.73193i	0.384501	+	0.443738i
$482$		0			0
$483$	−2.14979	+	1.38158i	−0.0978186	+	0.0628642i
$484$		0			0
$485$	8.43411	−	18.4681i	0.382973	−	0.838595i
$486$		0			0
$487$	5.92522	−	3.80790i	0.268497	−	0.172553i	−0.399464	−	0.916749i	$-0.630804\pi$
$487$	5.92522	−	3.80790i	0.268497	−	0.172553i	0.667961	+	0.744196i	$0.267167\pi$
$488$		0			0
$489$	−2.67010	−	18.5710i	−0.120746	−	0.839809i
$490$		0			0
$491$	−1.35208	+	9.40389i	−0.0610183	+	0.424392i	0.936300	+	0.351202i	$0.114227\pi$
$491$	−1.35208	+	9.40389i	−0.0610183	+	0.424392i	−0.997318	+	0.0731898i	$0.976682\pi$
$492$		0			0
$493$	24.3606	+	15.6556i	1.09715	+	0.705094i
$494$		0			0
$495$	5.08273	+	3.26647i	0.228452	+	0.146817i
$496$		0			0
$497$	−0.508164	+	0.586452i	−0.0227943	+	0.0263060i
$498$		0			0
$499$	6.67323			0.298735			0.149367	−	0.988782i	$-0.452276\pi$
$499$	6.67323			0.298735			0.149367	+	0.988782i	$0.452276\pi$
$500$		0			0
$501$	−1.69866	+	11.8144i	−0.0758904	+	0.527830i
$502$		0			0
$503$	18.7005	+	5.49097i	0.833815	+	0.244830i	0.670655	−	0.741769i	$-0.266013\pi$
$503$	18.7005	+	5.49097i	0.833815	+	0.244830i	0.163160	+	0.986600i	$0.447831\pi$
$504$		0			0
$505$	9.72204	−	11.2198i	0.432625	−	0.499276i
$506$		0			0
$507$	−3.29031			−0.146128
$508$		0			0
$509$	4.90861	+	10.7484i	0.217570	+	0.476413i	0.986674	−	0.162712i	$-0.0520241\pi$
$509$	4.90861	+	10.7484i	0.217570	+	0.476413i	−0.769103	+	0.639125i	$0.779297\pi$
$510$		0			0
$511$	−4.18333	−	4.82782i	−0.185060	−	0.213570i
$512$		0			0
$513$	−0.185664	−	1.29132i	−0.00819728	−	0.0570133i
$514$		0			0
$515$	1.79392	+	3.92814i	0.0790496	+	0.173095i
$516$		0			0
$517$	−37.1149	−	10.8979i	−1.63231	−	0.479289i
$518$		0			0
$519$	15.6407	+	10.0517i	0.686552	+	0.441220i
$520$		0			0
$521$	−1.69982	−	0.499113i	−0.0744706	−	0.0218665i	0.244285	−	0.969703i	$-0.421447\pi$
$521$	−1.69982	−	0.499113i	−0.0744706	−	0.0218665i	−0.318756	+	0.947837i	$0.603265\pi$
$522$		0			0
$523$	24.3294	+	28.0777i	1.06385	+	1.22775i	0.972737	+	0.231910i	$0.0744974\pi$
$523$	24.3294	+	28.0777i	1.06385	+	1.22775i	0.0911143	+	0.995840i	$0.470957\pi$
$524$		0			0
$525$	1.26765	−	2.77578i	0.0553250	−	0.121145i
$526$		0			0
$527$	−10.2958	+	3.02312i	−0.448493	+	0.131689i
$528$		0			0
$529$	14.5910	−	4.28431i	0.634392	−	0.186274i
$530$		0			0
$531$	−0.438016	+	0.959121i	−0.0190083	+	0.0416223i
$532$		0			0
$533$	−6.51198	−	45.2918i	−0.282065	−	1.96181i
$534$		0			0
$535$	−22.9306			−0.991376
$536$		0			0
$537$	−1.74006			−0.0750893
$538$		0			0
$539$	−4.10434	−	28.5463i	−0.176786	−	1.22958i
$540$		0			0
$541$	−14.1105	+	30.8977i	−0.606659	+	1.32840i	0.318178	+	0.948031i	$0.396929\pi$
$541$	−14.1105	+	30.8977i	−0.606659	+	1.32840i	−0.924836	+	0.380366i	$0.875798\pi$
$542$		0			0
$543$	−8.51724	+	2.50089i	−0.365510	+	0.107323i
$544$		0			0
$545$	−23.2090	+	6.81476i	−0.994162	+	0.291912i
$546$		0			0
$547$	−14.2268	+	31.1523i	−0.608292	+	1.33197i	0.315443	+	0.948944i	$0.397847\pi$
$547$	−14.2268	+	31.1523i	−0.608292	+	1.33197i	−0.923736	+	0.383030i	$0.874881\pi$
$548$		0			0
$549$	9.02352	+	10.4137i	0.385115	+	0.444446i
$550$		0			0
$551$	−5.74022	−	1.68548i	−0.244542	−	0.0718039i
$552$		0			0
$553$	−4.88206	−	3.13751i	−0.207606	−	0.133420i
$554$		0			0
$555$	3.95183	+	1.16036i	0.167746	+	0.0492547i
$556$		0			0
$557$	−14.2264	−	31.1514i	−0.602791	−	1.31993i	−0.927397	−	0.374079i	$-0.877959\pi$
$557$	−14.2264	−	31.1514i	−0.602791	−	1.31993i	0.324606	−	0.945849i	$-0.394768\pi$
$558$		0			0
$559$	6.27509	+	43.6442i	0.265408	+	1.84595i
$560$		0			0
$561$	19.3540	+	22.3357i	0.817128	+	0.943015i
$562$		0			0
$563$	5.74664	+	12.5834i	0.242192	+	0.530326i	0.991222	−	0.132210i	$-0.0422074\pi$
$563$	5.74664	+	12.5834i	0.242192	+	0.530326i	−0.749030	+	0.662536i	$0.769480\pi$
$564$		0			0
$565$	0.688520			0.0289662
$566$		0			0
$567$	−0.599466	+	0.691821i	−0.0251752	+	0.0290538i
$568$		0			0
$569$	−22.8778	−	6.71752i	−0.959086	−	0.281613i	−0.235521	−	0.971869i	$-0.575680\pi$
$569$	−22.8778	−	6.71752i	−0.959086	−	0.281613i	−0.723565	+	0.690256i	$0.757498\pi$
$570$		0			0
$571$	−2.86947	+	19.9576i	−0.120083	+	0.835199i	0.837375	+	0.546628i	$0.184089\pi$
$571$	−2.86947	+	19.9576i	−0.120083	+	0.835199i	−0.957459	+	0.288570i	$0.906820\pi$
$572$		0			0
$573$	−4.88933			−0.204255
$574$		0			0
$575$	6.09402	−	7.03288i	0.254138	−	0.293291i
$576$		0			0
$577$	38.5138	+	24.7513i	1.60335	+	1.03041i	0.965552	+	0.260209i	$0.0837915\pi$
$577$	38.5138	+	24.7513i	1.60335	+	1.03041i	0.637799	+	0.770203i	$0.279845\pi$
$578$		0			0
$579$	−12.8338	−	8.24781i	−0.533356	−	0.342767i
$580$		0			0
$581$	0.633859	−	4.40859i	0.0262969	−	0.182899i
$582$		0			0
$583$	−8.59784	−	59.7993i	−0.356086	−	2.47663i
$584$		0			0
$585$	−4.38321	+	2.81692i	−0.181223	+	0.116465i
$586$		0			0
$587$	−5.08565	+	11.1360i	−0.209907	+	0.459633i	−0.985076	−	0.172122i	$-0.944938\pi$
$587$	−5.08565	+	11.1360i	−0.209907	+	0.459633i	0.775169	+	0.631755i	$0.217665\pi$
$588$		0			0
$589$	1.86497	−	1.19854i	0.0768446	−	0.0493851i
$590$		0			0
$591$	−7.47765	−	8.62967i	−0.307589	−	0.354977i
$592$		0			0
$593$	2.72655	−	18.9636i	0.111966	−	0.778740i	−0.854038	−	0.520211i	$-0.825853\pi$
$593$	2.72655	−	18.9636i	0.111966	−	0.778740i	0.966003	−	0.258529i	$-0.0832378\pi$
$594$		0			0
$595$	−4.88673	+	5.63958i	−0.200336	+	0.231200i
$596$		0			0
$597$	0.731126	+	1.60094i	0.0299230	+	0.0655222i
$598$		0			0
$599$	−6.64809	+	4.27247i	−0.271634	+	0.174568i	−0.669365	−	0.742933i	$-0.733434\pi$
$599$	−6.64809	+	4.27247i	−0.271634	+	0.174568i	0.397732	+	0.917502i	$0.369798\pi$
$600$		0			0
$601$	45.8502	−	13.4628i	1.87027	−	0.549160i	0.872054	−	0.489410i	$-0.162788\pi$
$601$	45.8502	−	13.4628i	1.87027	−	0.549160i	0.998213	−	0.0597497i	$-0.0190303\pi$
$602$		0			0
$603$	−3.74407	+	7.27887i	−0.152470	+	0.296418i
$604$		0			0
$605$	13.5070	−	3.96601i	0.549138	−	0.161241i
$606$		0			0
$607$	31.8022	−	20.4381i	1.29081	−	0.829555i	0.298633	−	0.954368i	$-0.403469\pi$
$607$	31.8022	−	20.4381i	1.29081	−	0.829555i	0.992180	+	0.124813i	$0.0398331\pi$
$608$		0			0
$609$	1.74384	+	3.81848i	0.0706640	+	0.154733i
$610$		0			0
$611$	21.8449	−	25.2104i	0.883750	−	1.01990i
$612$		0			0
$613$	1.67191	−	11.6284i	0.0675277	−	0.469665i	−0.927797	−	0.373084i	$-0.878300\pi$
$613$	1.67191	−	11.6284i	0.0675277	−	0.469665i	0.995325	−	0.0965811i	$-0.0307907\pi$
$614$		0			0
$615$	−9.58402	−	11.0605i	−0.386465	−	0.446004i
$616$		0			0
$617$	−7.59820	+	4.88307i	−0.305892	+	0.196585i	−0.684577	−	0.728941i	$-0.740013\pi$
$617$	−7.59820	+	4.88307i	−0.305892	+	0.196585i	0.378685	+	0.925526i	$0.376377\pi$
$618$		0			0
$619$	11.0328	−	24.1584i	0.443445	−	0.971009i	−0.547508	−	0.836800i	$-0.684424\pi$
$619$	11.0328	−	24.1584i	0.443445	−	0.971009i	0.990953	−	0.134209i	$-0.0428492\pi$
$620$		0			0
$621$	−2.34844	+	1.50925i	−0.0942396	+	0.0605641i
$622$		0			0
$623$	−0.786108	−	5.46750i	−0.0314947	−	0.219051i
$624$		0			0
$625$	−0.395625	+	2.75163i	−0.0158250	+	0.110065i
$626$		0			0
$627$	−5.13659	−	3.30108i	−0.205135	−	0.131833i
$628$		0			0
$629$	16.9487	+	10.8923i	0.675789	+	0.434303i
$630$		0			0
$631$	17.4120	−	20.0946i	0.693162	−	0.799952i	−0.294649	−	0.955605i	$-0.595203\pi$
$631$	17.4120	−	20.0946i	0.693162	−	0.799952i	0.987812	+	0.155653i	$0.0497483\pi$
$632$		0			0
$633$	9.55312			0.379703
$634$		0			0
$635$	−2.79028	+	19.4069i	−0.110729	+	0.770137i
$636$		0			0
$637$	23.8633	+	7.00689i	0.945497	+	0.277623i
$638$		0			0
$639$	−0.555121	+	0.640644i	−0.0219603	+	0.0253435i
$640$		0			0
$641$	1.86764			0.0737675			0.0368837	−	0.999320i	$-0.488257\pi$
$641$	1.86764			0.0737675			0.0368837	+	0.999320i	$0.488257\pi$
$642$		0			0
$643$	−10.6907	−	23.4093i	−0.421599	−	0.923173i	−0.994616	−	0.103630i	$-0.966954\pi$
$643$	−10.6907	−	23.4093i	−0.421599	−	0.923173i	0.573017	−	0.819544i	$-0.305773\pi$
$644$		0			0
$645$	9.23538	+	10.6582i	0.363643	+	0.419666i
$646$		0			0
$647$	−3.86134	−	26.8562i	−0.151805	−	1.05583i	−0.913192	−	0.407529i	$-0.866390\pi$
$647$	−3.86134	−	26.8562i	−0.151805	−	1.05583i	0.761387	−	0.648297i	$-0.224519\pi$
$648$		0			0
$649$	2.05003	+	4.48893i	0.0804705	+	0.176206i
$650$		0			0
$651$	−1.49253	−	0.438247i	−0.0584970	−	0.0171763i
$652$		0			0
$653$	−34.3930	−	22.1030i	−1.34590	−	0.864958i	−0.348522	−	0.937301i	$-0.613316\pi$
$653$	−34.3930	−	22.1030i	−1.34590	−	0.864958i	−0.997380	+	0.0723425i	$0.976953\pi$
$654$		0			0
$655$	−17.8590	−	5.24388i	−0.697810	−	0.204895i
$656$		0			0
$657$	−4.56989	−	5.27394i	−0.178288	−	0.205756i
$658$		0			0
$659$	−11.4622	+	25.0987i	−0.446504	+	0.977708i	0.543854	+	0.839180i	$0.316965\pi$
$659$	−11.4622	+	25.0987i	−0.446504	+	0.977708i	−0.990358	+	0.138529i	$0.955763\pi$
$660$		0			0
$661$	36.1468	−	10.6137i	1.40595	−	0.412823i	0.511225	−	0.859447i	$-0.329192\pi$
$661$	36.1468	−	10.6137i	1.40595	−	0.412823i	0.894722	+	0.446623i	$0.147374\pi$
$662$		0			0
$663$	−24.4545	+	7.18050i	−0.949736	+	0.278868i
$664$		0			0
$665$	0.640437	−	1.40236i	0.0248351	−	0.0543813i
$666$		0			0
$667$	1.82184	+	12.6712i	0.0705421	+	0.490631i
$668$		0			0
$669$	20.5770			0.795554
$670$		0			0
$671$	64.4906			2.48963
$672$		0			0
$673$	−0.740340	−	5.14918i	−0.0285380	−	0.198486i	0.970565	−	0.240841i	$-0.0774232\pi$
$673$	−0.740340	−	5.14918i	−0.0285380	−	0.198486i	−0.999103	+	0.0423546i	$0.986514\pi$
$674$		0			0
$675$	1.38479	−	3.03227i	0.0533007	−	0.116712i
$676$		0			0
$677$	17.1129	−	5.02479i	0.657701	−	0.193119i	0.0641819	−	0.997938i	$-0.479556\pi$
$677$	17.1129	−	5.02479i	0.657701	−	0.193119i	0.593519	+	0.804820i	$0.297738\pi$
$678$		0			0
$679$	13.8138	−	4.05611i	0.530127	−	0.155659i
$680$		0			0
$681$	−10.7453	+	23.5290i	−0.411763	+	0.901634i
$682$		0			0
$683$	−10.4179	−	12.0230i	−0.398632	−	0.460046i	0.520578	−	0.853814i	$-0.325717\pi$
$683$	−10.4179	−	12.0230i	−0.398632	−	0.460046i	−0.919210	+	0.393769i	$0.871171\pi$
$684$		0			0
$685$	−3.16657	−	0.929790i	−0.120989	−	0.0355255i
$686$		0			0
$687$	10.4397	+	6.70919i	0.398300	+	0.255972i
$688$		0			0
$689$	49.9892	+	14.6782i	1.90444	+	0.559193i
$690$		0			0
$691$	9.96608	+	21.8227i	0.379127	+	0.830173i	0.998967	+	0.0454445i	$0.0144704\pi$
$691$	9.96608	+	21.8227i	0.379127	+	0.830173i	−0.619839	+	0.784729i	$0.712802\pi$
$692$		0			0
$693$	0.609727	+	4.24074i	0.0231616	+	0.161093i
$694$		0			0
$695$	5.78919	+	6.68108i	0.219596	+	0.253428i
$696$		0			0
$697$	−29.7395	−	65.1204i	−1.12646	−	2.46661i
$698$		0			0
$699$	−5.50511			−0.208222
$700$		0			0
$701$	0.626793	−	0.723358i	0.0236736	−	0.0273208i	−0.743789	−	0.668414i	$-0.766973\pi$
$701$	0.626793	−	0.723358i	0.0236736	−	0.0273208i	0.767463	+	0.641093i	$0.221519\pi$
$702$		0			0
$703$	−3.99371	−	1.17266i	−0.150626	−	0.0442277i
$704$		0			0
$705$	1.51840	−	10.5607i	0.0571864	−	0.397740i
$706$		0			0
$707$	10.5275			0.395926
$708$		0			0
$709$	−0.228790	+	0.264038i	−0.00859240	+	0.00991616i	−0.760030	−	0.649889i	$-0.774816\pi$
$709$	−0.228790	+	0.264038i	−0.00859240	+	0.00991616i	0.751437	+	0.659805i	$0.229361\pi$
$710$		0			0
$711$	−5.33319	−	3.42743i	−0.200010	−	0.128539i
$712$		0			0
$713$	−3.99067	−	2.56465i	−0.149452	−	0.0960467i
$714$		0			0
$715$	−3.47044	+	24.1374i	−0.129787	+	0.902689i
$716$		0			0
$717$	−2.50994	−	17.4570i	−0.0937355	−	0.651944i
$718$		0			0
$719$	−28.6986	+	18.4435i	−1.07028	+	0.687827i	−0.952292	−	0.305189i	$-0.901281\pi$
$719$	−28.6986	+	18.4435i	−1.07028	+	0.687827i	−0.117987	+	0.993015i	$0.537644\pi$
$720$		0			0
$721$	−1.27209	+	2.78550i	−0.0473752	+	0.103737i
$722$		0			0
$723$	−21.4165	+	13.7635i	−0.796487	+	0.511871i
$724$		0			0
$725$	−10.0106	−	11.5529i	−0.371785	−	0.429062i
$726$		0			0
$727$	−5.90672	+	41.0822i	−0.219068	+	1.52365i	0.522421	+	0.852688i	$0.325029\pi$
$727$	−5.90672	+	41.0822i	−0.219068	+	1.52365i	−0.741489	+	0.670965i	$0.765880\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	28.6576	+	62.7515i	1.05994	+	2.32095i
$732$		0			0
$733$	2.89542	−	1.86078i	0.106945	−	0.0687293i	−0.486075	−	0.873917i	$-0.661572\pi$
$733$	2.89542	−	1.86078i	0.106945	−	0.0687293i	0.593020	+	0.805188i	$0.297935\pi$
$734$		0			0
$735$	7.63248	−	2.24110i	0.281528	−	0.0826641i
$736$		0			0
$737$	14.2708	+	35.5523i	0.525673	+	1.30958i
$738$		0			0
$739$	12.5370	−	3.68120i	0.461182	−	0.135415i	−0.0428848	−	0.999080i	$-0.513655\pi$
$739$	12.5370	−	3.68120i	0.461182	−	0.135415i	0.504066	+	0.863665i	$0.331837\pi$
$740$		0			0
$741$	4.42965	−	2.84677i	0.162727	−	0.104579i
$742$		0			0
$743$	−0.112560	−	0.246471i	−0.00412941	−	0.00904216i	0.907556	−	0.419931i	$-0.137946\pi$
$743$	−0.112560	−	0.246471i	−0.00412941	−	0.00904216i	−0.911685	+	0.410889i	$0.865218\pi$
$744$		0			0
$745$	−2.44845	+	2.82566i	−0.0897041	+	0.103524i
$746$		0			0
$747$	0.692431	−	4.81597i	0.0253347	−	0.176207i
$748$		0			0
$749$	−10.6483	−	12.2888i	−0.389080	−	0.449022i
$750$		0			0
$751$	0.955593	−	0.614123i	0.0348701	−	0.0224097i	−0.523090	−	0.852278i	$-0.675221\pi$
$751$	0.955593	−	0.614123i	0.0348701	−	0.0224097i	0.557960	+	0.829868i	$0.311584\pi$
$752$		0			0
$753$	0.266212	−	0.582924i	0.00970131	−	0.0212429i
$754$		0			0
$755$	−15.9704	+	10.2635i	−0.581222	+	0.373529i
$756$		0			0
$757$	7.19178	+	50.0199i	0.261390	+	1.81800i	0.522436	+	0.852678i	$0.325023\pi$
$757$	7.19178	+	50.0199i	0.261390	+	1.81800i	−0.261046	+	0.965326i	$0.584068\pi$
$758$		0			0
$759$	−1.85940	+	12.9324i	−0.0674918	+	0.469416i
$760$		0			0
$761$	11.4862	+	7.38174i	0.416375	+	0.267588i	0.732011	−	0.681292i	$-0.238582\pi$
$761$	11.4862	+	7.38174i	0.416375	+	0.267588i	−0.315637	+	0.948880i	$0.602218\pi$
$762$		0			0
$763$	−14.4297	−	9.27338i	−0.522389	−	0.335719i
$764$		0			0
$765$	−5.33829	+	6.16072i	−0.193006	+	0.222741i
$766$		0			0
$767$	−4.25571			−0.153665
$768$		0			0
$769$	−0.475579	+	3.30773i	−0.0171498	+	0.119280i	−0.996598	−	0.0824164i	$-0.973736\pi$
$769$	−0.475579	+	3.30773i	−0.0171498	+	0.119280i	0.979448	+	0.201696i	$0.0646453\pi$
$770$		0			0
$771$	18.5822	+	5.45623i	0.669222	+	0.196501i
$772$		0			0
$773$	−25.6925	+	29.6508i	−0.924096	+	1.06646i	0.0735089	+	0.997295i	$0.476580\pi$
$773$	−25.6925	+	29.6508i	−0.924096	+	1.06646i	−0.997605	+	0.0691692i	$0.977965\pi$
$774$		0			0
$775$	5.66459			0.203478
$776$		0			0
$777$	1.21326	+	2.65667i	0.0435255	+	0.0953076i
$778$		0			0
$779$	9.68558	+	11.1777i	0.347022	+	0.400484i
$780$		0			0
$781$	0.564623	+	3.92704i	0.0202038	+	0.140520i
$782$		0			0
$783$	1.90498	+	4.17133i	0.0680785	+	0.149071i
$784$		0			0
$785$	−2.78209	−	0.816895i	−0.0992970	−	0.0291562i
$786$		0			0
$787$	11.9881	+	7.70428i	0.427329	+	0.274628i	0.736577	−	0.676354i	$-0.236441\pi$
$787$	11.9881	+	7.70428i	0.427329	+	0.274628i	−0.309248	+	0.950982i	$0.600077\pi$
$788$		0			0
$789$	24.6248	+	7.23050i	0.876667	+	0.257413i
$790$		0			0
$791$	0.319728	+	0.368986i	0.0113682	+	0.0131196i
$792$		0			0
$793$	−23.1033	+	50.5892i	−0.820422	+	1.79647i
$794$		0			0
$795$	15.9887	−	4.69469i	0.567059	−	0.166504i
$796$		0			0
$797$	27.1945	−	7.98502i	0.963278	−	0.282844i	0.237973	−	0.971272i	$-0.423517\pi$
$797$	27.1945	−	7.98502i	0.963278	−	0.282844i	0.725305	+	0.688428i	$0.241699\pi$
$798$		0			0
$799$	21.6806	−	47.4739i	0.767005	−	1.67951i
$800$		0			0
$801$	−0.858749	−	5.97273i	−0.0303424	−	0.211036i
$802$		0			0
$803$	−32.6608			−1.15257
$804$		0			0
$805$	−3.29890			−0.116271
$806$		0			0
$807$	−2.51085	−	17.4633i	−0.0883861	−	0.614739i
$808$		0			0
$809$	18.7702	−	41.1009i	0.659924	−	1.44503i	−0.222669	−	0.974894i	$-0.571477\pi$
$809$	18.7702	−	41.1009i	0.659924	−	1.44503i	0.882593	−	0.470138i	$-0.155796\pi$
$810$		0			0
$811$	42.0405	−	12.3442i	1.47624	−	0.433464i	0.558119	−	0.829761i	$-0.311523\pi$
$811$	42.0405	−	12.3442i	1.47624	−	0.433464i	0.918122	+	0.396297i	$0.129705\pi$
$812$		0			0
$813$	−10.3950	+	3.05224i	−0.364568	+	0.107047i
$814$		0			0
$815$	10.0615	−	22.0315i	0.352437	−	0.771730i
$816$		0			0
$817$	−9.33324	−	10.7711i	−0.326529	−	0.376834i
$818$		0			0
$819$	−3.54505	−	1.04092i	−0.123874	−	0.0363727i
$820$		0			0
$821$	19.4989	+	12.5312i	0.680518	+	0.437342i	0.834703	−	0.550700i	$-0.185639\pi$
$821$	19.4989	+	12.5312i	0.680518	+	0.437342i	−0.154186	+	0.988042i	$0.549275\pi$
$822$		0			0
$823$	14.0387	+	4.12214i	0.489359	+	0.143689i	0.517098	−	0.855926i	$-0.327012\pi$
$823$	14.0387	+	4.12214i	0.489359	+	0.143689i	−0.0277384	+	0.999615i	$0.508831\pi$
$824$		0			0
$825$	−6.48118	−	14.1918i	−0.225646	−	0.494096i
$826$		0			0
$827$	−4.42953	−	30.8081i	−0.154030	−	1.07130i	−0.909376	−	0.415975i	$-0.863440\pi$
$827$	−4.42953	−	30.8081i	−0.154030	−	1.07130i	0.755346	−	0.655326i	$-0.227469\pi$
$828$		0			0
$829$	21.8685	+	25.2375i	0.759523	+	0.876536i	0.995455	−	0.0952335i	$-0.0303598\pi$
$829$	21.8685	+	25.2375i	0.759523	+	0.876536i	−0.235932	+	0.971770i	$0.575814\pi$
$830$		0			0
$831$	7.72019	+	16.9049i	0.267810	+	0.586423i
$832$		0			0
$833$	38.9113			1.34820
$834$		0			0
$835$	−10.0903	+	11.6449i	−0.349190	+	0.402987i
$836$		0			0
$837$	−1.63045	−	0.478744i	−0.0563567	−	0.0165478i
$838$		0			0
$839$	−8.11244	+	56.4232i	−0.280072	+	1.94795i	0.0363800	+	0.999338i	$0.488417\pi$
$839$	−8.11244	+	56.4232i	−0.280072	+	1.94795i	−0.316452	+	0.948608i	$0.602492\pi$
$840$		0			0
$841$	−7.97107			−0.274864
$842$		0			0
$843$	4.54316	−	5.24308i	0.156475	−	0.180581i
$844$		0			0
$845$	−3.57326	−	2.29640i	−0.122924	−	0.0789984i
$846$		0			0
$847$	8.39768	+	5.39686i	0.288548	+	0.185438i
$848$		0			0
$849$	1.61060	−	11.2020i	0.0552757	−	0.384451i
$850$		0			0
$851$	1.26753	+	8.81588i	0.0434505	+	0.302205i
$852$		0			0
$853$	23.9866	−	15.4153i	0.821286	−	0.527808i	−0.0612120	−	0.998125i	$-0.519497\pi$
$853$	23.9866	−	15.4153i	0.821286	−	0.527808i	0.882498	+	0.470316i	$0.155860\pi$
$854$		0			0
$855$	0.699618	−	1.53195i	0.0239264	−	0.0523916i
$856$		0			0
$857$	37.4772	−	24.0851i	1.28020	−	0.822733i	0.289285	−	0.957243i	$-0.406583\pi$
$857$	37.4772	−	24.0851i	1.28020	−	0.822733i	0.990912	+	0.134510i	$0.0429462\pi$
$858$		0			0
$859$	−26.6840	−	30.7949i	−0.910445	−	1.05071i	−0.998509	−	0.0545952i	$-0.982613\pi$
$859$	−26.6840	−	30.7949i	−0.910445	−	1.05071i	0.0880631	−	0.996115i	$-0.471932\pi$
$860$		0			0
$861$	1.47694	−	10.2724i	0.0503341	−	0.350082i
$862$		0			0
$863$	−11.9027	+	13.7365i	−0.405173	+	0.467595i	−0.921263	−	0.388939i	$-0.872842\pi$
$863$	−11.9027	+	13.7365i	−0.405173	+	0.467595i	0.516090	+	0.856534i	$0.327387\pi$
$864$		0			0
$865$	9.97040	+	21.8321i	0.339004	+	0.742315i
$866$		0			0
$867$	−19.2441	+	12.3674i	−0.653563	+	0.420019i
$868$		0			0
$869$	−28.4689	+	8.35923i	−0.965742	+	0.283568i
$870$		0			0
$871$	−33.0011	−	1.54170i	−1.11820	−	0.0522384i
$872$		0			0
$873$	15.0903	−	4.43092i	0.510730	−	0.149964i
$874$		0			0
$875$	8.28460	−	5.32419i	0.280071	−	0.179990i
$876$		0			0
$877$	12.4408	+	27.2415i	0.420094	+	0.919879i	0.994831	+	0.101540i	$0.0323771\pi$
$877$	12.4408	+	27.2415i	0.420094	+	0.919879i	−0.574737	+	0.818338i	$0.694896\pi$
$878$		0			0
$879$	22.3591	−	25.8038i	0.754153	−	0.870339i
$880$		0			0
$881$	4.60231	−	32.0097i	0.155056	−	1.07844i	−0.752527	−	0.658562i	$-0.771165\pi$
$881$	4.60231	−	32.0097i	0.155056	−	1.07844i	0.907582	−	0.419874i	$-0.137926\pi$
$882$		0			0
$883$	2.87319	+	3.31584i	0.0966905	+	0.111587i	0.802033	−	0.597280i	$-0.203752\pi$
$883$	2.87319	+	3.31584i	0.0966905	+	0.111587i	−0.705342	+	0.708867i	$0.749207\pi$
$884$		0			0
$885$	−1.14508	+	0.735897i	−0.0384914	+	0.0247369i
$886$		0			0
$887$	7.04191	−	15.4196i	0.236444	−	0.517741i	−0.753796	−	0.657108i	$-0.771780\pi$
$887$	7.04191	−	15.4196i	0.236444	−	0.517741i	0.990241	+	0.139367i	$0.0445068\pi$
$888$		0			0
$889$	−11.6961	+	7.51662i	−0.392274	+	0.252099i
$890$		0			0
$891$	0.666070	+	4.63262i	0.0223142	+	0.155198i
$892$		0			0
$893$	−1.53449	+	10.6726i	−0.0513499	+	0.357146i
$894$		0			0
$895$	−1.88970	−	1.21444i	−0.0631657	−	0.0405941i
$896$		0			0
$897$	−9.47860	−	6.09152i	−0.316481	−	0.203390i
$898$		0			0
$899$	−5.10298	+	5.88915i	−0.170194	+	0.196414i
$900$		0			0
$901$	81.5122			2.71557
$902$		0			0
$903$	−1.42322	+	9.89870i	−0.0473617	+	0.329408i
$904$		0			0
$905$	−10.9951	−	3.22845i	−0.365490	−	0.107317i
$906$		0			0
$907$	−22.3807	+	25.8287i	−0.743140	+	0.857629i	−0.993885	−	0.110424i	$-0.964779\pi$
$907$	−22.3807	+	25.8287i	−0.743140	+	0.857629i	0.250745	+	0.968053i	$0.419325\pi$
$908$		0			0
$909$	11.5003			0.381440
$910$		0			0
$911$	−6.60586	−	14.4648i	−0.218862	−	0.479241i	0.768073	−	0.640363i	$-0.221216\pi$
$911$	−6.60586	−	14.4648i	−0.218862	−	0.479241i	−0.986934	+	0.161122i	$0.948489\pi$
$912$		0			0
$913$	−14.9123	−	17.2097i	−0.493525	−	0.569559i
$914$		0			0
$915$	2.53150	+	17.6070i	0.0836888	+	0.582068i
$916$		0			0
$917$	−5.48294	−	12.0060i	−0.181063	−	0.396472i
$918$		0			0
$919$	−39.1542	−	11.4967i	−1.29158	−	0.379241i	−0.437420	−	0.899257i	$-0.644108\pi$
$919$	−39.1542	−	11.4967i	−1.29158	−	0.379241i	−0.854157	+	0.520016i	$0.825926\pi$
$920$		0			0
$921$	−18.4592	−	11.8630i	−0.608252	−	0.390900i
$922$		0			0
$923$	−3.28281	−	0.963919i	−0.108055	−	0.0317278i
$924$		0			0
$925$	−6.96479	−	8.03780i	−0.229001	−	0.264281i
$926$		0			0
$927$	−1.38964	+	3.04289i	−0.0456418	+	0.0999417i
$928$		0			0
$929$	−27.8507	+	8.17769i	−0.913751	+	0.268301i	−0.704619	−	0.709586i	$-0.748882\pi$
$929$	−27.8507	+	8.17769i	−0.913751	+	0.268301i	−0.209132	+	0.977887i	$0.567064\pi$
$930$		0			0
$931$	−7.71336	+	2.26485i	−0.252795	+	0.0742273i
$932$		0			0
$933$	2.35664	−	5.16031i	0.0771528	−	0.168941i
$934$		0			0
$935$	5.42966	+	37.7641i	0.177569	+	1.23502i
$936$		0			0
$937$	−26.1874			−0.855506			−0.427753	−	0.903896i	$-0.640695\pi$
$937$	−26.1874			−0.855506			−0.427753	+	0.903896i	$0.640695\pi$
$938$		0			0
$939$	−1.53180			−0.0499885
$940$		0			0
$941$	−2.64310	−	18.3832i	−0.0861628	−	0.599275i	−0.986460	−	0.164000i	$-0.947560\pi$
$941$	−2.64310	−	18.3832i	−0.0861628	−	0.599275i	0.900298	−	0.435275i	$-0.143349\pi$
$942$		0			0
$943$	13.1472	−	28.7883i	0.428131	−	0.937477i
$944$		0			0
$945$	−1.13386	+	0.332930i	−0.0368843	+	0.0108302i
$946$		0			0
$947$	0.641897	−	0.188478i	0.0208588	−	0.00612471i	−0.271286	−	0.962499i	$-0.587449\pi$
$947$	0.641897	−	0.188478i	0.0208588	−	0.00612471i	0.292145	+	0.956374i	$0.405631\pi$
$948$		0			0
$949$	11.7005	−	25.6205i	0.379814	−	0.831676i
$950$		0			0
$951$	7.74784	+	8.94148i	0.251241	+	0.289947i
$952$		0			0
$953$	15.5563	+	4.56775i	0.503919	+	0.147964i	0.523805	−	0.851838i	$-0.324512\pi$
$953$	15.5563	+	4.56775i	0.503919	+	0.147964i	−0.0198859	+	0.999802i	$0.506330\pi$
$954$		0			0
$955$	−5.30978	−	3.41239i	−0.171821	−	0.110422i
$956$		0			0
$957$	20.5930	+	6.04665i	0.665678	+	0.195461i
$958$		0			0
$959$	−0.972178	−	2.12877i	−0.0313933	−	0.0687416i
$960$		0			0
$961$	4.00082	+	27.8263i	0.129059	+	0.897622i
$962$		0			0
$963$	−11.6323	−	13.4243i	−0.374844	−	0.432593i
$964$		0			0
$965$	−8.18111	−	17.9141i	−0.263359	−	0.576677i
$966$		0			0
$967$	−2.70069			−0.0868483			−0.0434242	−	0.999057i	$-0.513827\pi$
$967$	−2.70069			−0.0868483			−0.0434242	+	0.999057i	$0.513827\pi$
$968$		0			0
$969$	5.39486	−	6.22600i	0.173308	−	0.200008i
$970$		0			0
$971$	42.5821	+	12.5032i	1.36652	+	0.401248i	0.881058	−	0.473008i	$-0.156832\pi$
$971$	42.5821	+	12.5032i	1.36652	+	0.401248i	0.485466	+	0.874256i	$0.338650\pi$
$972$		0			0
$973$	−0.892143	+	6.20499i	−0.0286008	+	0.198923i
$974$		0			0
$975$	13.4545			0.430889
$976$		0			0
$977$	−20.8501	+	24.0623i	−0.667054	+	0.769822i	−0.983912	−	0.178651i	$-0.942827\pi$
$977$	−20.8501	+	24.0623i	−0.667054	+	0.769822i	0.316858	+	0.948473i	$0.397372\pi$
$978$		0			0
$979$	−23.7581	−	15.2684i	−0.759313	−	0.487981i
$980$		0			0
$981$	−15.7631	−	10.1303i	−0.503276	−	0.323436i
$982$		0			0
$983$	4.99044	−	34.7093i	0.159170	−	1.10705i	−0.740996	−	0.671509i	$-0.765646\pi$
$983$	4.99044	−	34.7093i	0.159170	−	1.10705i	0.900167	−	0.435546i	$-0.143445\pi$
$984$		0			0
$985$	−2.09781	−	14.5906i	−0.0668419	−	0.464895i
$986$		0			0
$987$	6.36472	−	4.09036i	0.202591	−	0.130198i
$988$		0			0
$989$	−12.6689	+	27.7411i	−0.402849	+	0.882115i
$990$		0			0
$991$	16.1265	−	10.3639i	0.512276	−	0.329220i	−0.258834	−	0.965922i	$-0.583338\pi$
$991$	16.1265	−	10.3639i	0.512276	−	0.329220i	0.771110	+	0.636702i	$0.219702\pi$
$992$		0			0
$993$	−12.3011	−	14.1962i	−0.390363	−	0.450503i
$994$		0			0
$995$	−0.323341	+	2.24888i	−0.0102506	+	0.0712944i
$996$		0			0
$997$	2.94916	−	3.40352i	0.0934010	−	0.107790i	−0.707125	−	0.707089i	$-0.750008\pi$
$997$	2.94916	−	3.40352i	0.0934010	−	0.107790i	0.800526	+	0.599298i	$0.204554\pi$
$998$		0			0
$999$	1.32537	+	2.90217i	0.0419330	+	0.0918205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.625.2	yes	60
67.64	even	11	inner	804.2.q.b.265.2	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.265.2	✓	60	67.64	even	11	inner
804.2.q.b.625.2	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(-0.536269 + 1.17426i) q^{5} +(-0.878330 + 0.257901i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(-0.536269 + 1.17426i) q^{5} +(-0.878330 + 0.257901i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-1.94425 + 4.25731i) q^{11} +(-2.64310 - 3.05030i) q^{13} +(-1.23863 - 0.363695i) q^{15} +(-5.31227 - 3.41399i) q^{17} +(1.25176 + 0.367549i) q^{19} +(-0.380275 - 0.832687i) q^{21} +(-0.397285 - 2.76318i) q^{23} +(2.18299 + 2.51930i) q^{25} +(-0.415415 - 0.909632i) q^{27} -4.58573 q^{29} +(1.11279 - 1.28423i) q^{31} +(-4.49067 - 1.31858i) q^{33} +(0.168177 - 1.16970i) q^{35} -3.19048 q^{37} +(2.64310 - 3.05030i) q^{39} +(9.53729 + 6.12925i) q^{41} +(-9.19035 - 5.90628i) q^{43} +(0.183718 - 1.27778i) q^{45} +(1.17622 + 8.18076i) q^{47} +(-5.18382 + 3.33144i) q^{49} +(2.62322 - 5.74406i) q^{51} +(-10.8592 + 6.97877i) q^{53} +(-3.95657 - 4.56612i) q^{55} +(-0.185664 + 1.29132i) q^{57} +(0.690489 - 0.796867i) q^{59} +(-5.72413 - 12.5341i) q^{61} +(0.770092 - 0.494908i) q^{63} +(4.99927 - 1.46792i) q^{65} +(5.64310 - 5.92920i) q^{67} +(2.67852 - 0.786483i) q^{69} +(0.713125 - 0.458298i) q^{71} +(2.89894 + 6.34779i) q^{73} +(-2.18299 + 2.51930i) q^{75} +(0.609727 - 4.24074i) q^{77} +(4.15154 + 4.79113i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-2.02120 + 4.42580i) q^{83} +(6.85773 - 4.40719i) q^{85} +(-0.652618 - 4.53906i) q^{87} +(-0.858749 + 5.97273i) q^{89} +(3.10819 + 1.99751i) q^{91} +(1.42953 + 0.918703i) q^{93} +(-1.10288 + 1.27279i) q^{95} -15.7274 q^{97} +(0.666070 - 4.63262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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